The two scripts are called pazhaya lipi and puthiya
lipi. Puthiya lipi, which means "new script," is the script
that you've been learning all along. It's the main script used in all fonts (or
at least the Kerala and Manorama fonts) for writing Malayalam on the computer.
It was officially introduced in the 1970's, when it began to appear in school
textbooks. Unfortunately, school textbooks have ended up being one of the very
few writings where puthiya lipi is used. Puthiya lipi is used in:

1. all school textbooks that are in Malayalam (as
previously mentioned),

2. my site (duh!),

3. SOME books for learning Malayalam,

4. websites in Malayalam,

5. dictionaries (at least MY dictionaries!), and

6. SOME other books in Malayalam, depending on who
published them. For example, I recently got a book of riddles called Thiranyeduththa
Kadamkathhakal ("Selected Riddles") published by the H & C
Publishing House at Thrissur.

Pazhaya lipi, on the other hand, is more complicated. However, since
Malayalees have used this script for about 300-400 years, it's still more
commonly used, even though the use of puthiya lipi is growing in the
publishing companies. Pazhaya lipi can be found not only in literary
works, but also on street signs, shop windows, comic and song books...almost
anywhere Malayalam is written, except, of course, school textbooks, websites,
and perhaps dictionaries. Finally, if a Malayalee was writing a letter, chances
are that it would be in pazhaya lipi, since it's easier for handwriting.

Some other differences between the scripts:

1. How the vowel "r" is written (as a maatra)

2. How the vowel "uu" is written as a maatra (rules similar
to how u is written as a maatra)

3. Whether or not the vowel "u" can be used at the end of a word

4. How d (ra/rra) is written

So what do we do about these ÜßÉßµZ???
I would advise you to learn BOTH of the scripts, because a book in pazhaya
lipi is equally or more useful for learning Malayalam as one in puthiya
lipi and vice versa; better the benefit of both scripts rather than one or
the other! So why not learn a bit of ÉÝÏ
ÜßÉß?